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For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •

For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with parts a,b,c with solution and steps!

For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •
Transcribed Image Text:For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •
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